平衡二叉树的插入调整(C语言）

平衡二叉树的插入调整(C语言）

平衡二叉树的插入与调整

左右单旋

左右单旋

avltree Lrotation(avltree A) {
    
      /*左单旋*/
	avltree B = A->left;
	A->left = B->right;
	B->right = A;
	A->height = getheight(A);
	B->height = getheight(B);
	return B;
}
avltree Rrotation(avltree A) {
    
      /*右单旋*/
	avltree B = A->right;
	A->right = B->left;
	B->left = A;
	A->height = getheight(A);
	B->height = getheight(B);
	return B;
}
avltree LRrotation(avltree A) {
    
       /*左右单旋*/
	A->left = Rrotation(A->left);
	return Lrotation(A);
}
avltree RLrotation(avltree A) {
    
    
	A->right = Lrotation(A->right);
	return Rrotation(A);
}

平衡二叉树的插入

插入后递归出栈，二叉树从插入点依次向上判定结点是否平衡
关键点在于判定插入数插在不平衡点的什么子树，才能决定使用哪种旋转函数，因此需要与不平衡点的子节点再次比较

avltree insert(avltree t, int num) {
    
    
	if (!t) {
    
    
		t = (avltree)malloc(sizeof(struct treenode));
		t->data = num;
		t->left = NULL;
		t->right = NULL;
		t->height = 0;
	}   /*叶节点高为0*/
	else {
    
    
		if (num < t->data) {
    
     
			t->left = insert(t->left, num); 
			if (getheight(t->left) - getheight(t->right) == 2)
			{
    
    
				if (num < t->left->data) t = Lrotation(t);  /*插入左子树的左子树左单旋*/
				else t = LRrotation(t);
			}
		}  /*左子树插入并调整平衡*/
		else if (num > t->data) {
    
     
			t->right = insert(t->right, num);
			if (getheight(t->right) - getheight(t->left) == 2)
			{
    
    
				if (num > t->right->data) t = Rrotation(t); /*插入右子树的右子树左单旋*/
				else t = RLrotation(t);
			}
		}/*右子树插入并调整平衡*/
	}
	t->height = getheight(t);/*更新树高*/
	return t;
}

求树高函数

默认叶节点高度为0

typedef struct treenode *avltree;
struct treenode {
    
    
	avltree left;
	avltree right;
	int data;
	int height;
};
int max(int a, int b) {
    
    
	return (a > b ? a : b);
}
int getheight(avltree t) {
    
         /*求树高*/
	if (!t) return -1;
	else {
    
    
		int lheight = getheight(t->left);
		int rheight = getheight(t->right);
		return max(lheight, rheight) + 1;
	}
}